Restriction categories were introduced in [1]} as a general framework for reasoning about categories of partial maps. Cartesian restriction (CR) categories are those with a certain sort of formal finite product structure – restriction products – introduced in [2]}. Notably, the p-categories of [3]} arise as restriction categories with restriction products. Discrete cartesian restriction (DCR) categories – named for a similarity to categories of discrete topological spaces – arise in [4]} as the restriction categories with finite latent limits – again a sort of formal limit. DCR categories are closely connected to the discrete inverse categories considered in [5]} which are presentable in terms of semi-Frobenius algebras, being those special/separable commutative Frobenius algebras with neither a unit nor a counit.
